On the Spectrality and Spectral Expansion of the Non-self-adjoint Mathieu-Hill Operator in All Real Line

O. A. Veliev

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arXiv · 1906.04912

On the Spectrality and Spectral Expansion of the Non-self-adjoint Mathieu-Hill Operator in All Real Line

O. A. Veliev

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Abstract

In this paper we investigate the non-self-adjoint operator H generated in all real line by the Mathieu-Hill equation with a complex-valued potential. We find a necessary and sufficient conditions on the potential for which H has no spectral singularity at infinity and it is an asymptotically spectral operator. Moreover, we give a detailed classification, stated in term of the potential, for the form of the spectral decomposition of the operator H by investigating the essential spectral singularities.

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BibTeX RIS

O. A. Veliev. 2019-06-10. On the Spectrality and Spectral Expansion of the Non-self-adjoint Mathieu-Hill Operator in All Real Line. https://arxiv.org/abs/1906.04912

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